Geometry Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge

Consider a square ABCD with center O. Suppose an exterior triangle AEB is constructed such that angle AEB measures 90 degrees and angle ABE measures 53 degrees. The line EO is extended to intersect side CD at a point F. Find the measure of angle OFC.

Geometry Problem 1533: Uncover the relationship between angles in an exterior triangle and intersecting lines of a square

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Problem 1534

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Problem 1532

Geometry Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle!

Problem 1531

Geometry Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord

Problem 1530

Geometry Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure

Problem 1529

Geometry Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths

Problem 1528

Geometry Problem 1528: Cracking the Circle Code: Unveiling the Tangent and Angle of an Inscribed Circle within a 90-Degree Circular Sector

Thematic Poem:
Geometric Beauty: Discovering Cyclic Quadrilaterals and Angles in a Square

In a geometry problem, one may find,
A square with angles all aligned,
But a triangle on the outside,
Will make your geometric heart glide.

For angles of the triangle,
Will reveal what you need to see,
When lines intersect with such grace,
You'll see a cyclic quadrilateral take place.

The center of the square is where it's at,
It's where you'll find lines that match,
When extended beyond their length,
You'll find new angles with great strength.

So uncover the relationship true,
Between angles and lines that ensue,
For a geometric problem so fine,
Is where your love for math will shine.

If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.

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